function [J grad] = nnCostFunction(nn_params, ...
                                   input_layer_size, ...
                                   hidden_layer_size, ...
                                   num_labels, ...
                                   X, y, lambda)
%NNCOSTFUNCTION Implements the neural network cost function for a two layer
%neural network which performs classification
%   [J grad] = NNCOSTFUNCTON(nn_params, hidden_layer_size, num_labels, ...
%   X, y, lambda) computes the cost and gradient of the neural network. The
%   parameters for the neural network are "unrolled" into the vector
%   nn_params and need to be converted back into the weight matrices. 
% 
%   The returned parameter grad should be a "unrolled" vector of the
%   partial derivatives of the neural network.
%

% Reshape nn_params back into the parameters Theta1 and Theta2, the weight matrices
% for our 2 layer neural network
Theta1 = reshape(nn_params(1:hidden_layer_size * (input_layer_size + 1)), ...
                 hidden_layer_size, (input_layer_size + 1));

Theta2 = reshape(nn_params((1 + (hidden_layer_size * (input_layer_size + 1))):end), ...
                 num_labels, (hidden_layer_size + 1));

% Setup some useful variables
m = size(X, 1);
         
% You need to return the following variables correctly 
J = 0;
Theta1_grad = zeros(size(Theta1));
Theta2_grad = zeros(size(Theta2));

% ====================== YOUR CODE HERE ======================
% Instructions: You should complete the code by working through the
%               following parts.
%
% Part 1: Feedforward the neural network and return the cost in the
%         variable J. After implementing Part 1, you can verify that your
%         cost function computation is correct by verifying the cost
%         computed in ex4.m
%
% Part 2: Implement the backpropagation algorithm to compute the gradients
%         Theta1_grad and Theta2_grad. You should return the partial derivatives of
%         the cost function with respect to Theta1 and Theta2 in Theta1_grad and
%         Theta2_grad, respectively. After implementing Part 2, you can check
%         that your implementation is correct by running checkNNGradients
%
%         Note: The vector y passed into the function is a vector of labels
%               containing values from 1..K. You need to map this vector into a 
%               binary vector of 1's and 0's to be used with the neural network
%               cost function.
%
%         Hint: We recommend implementing backpropagation using a for-loop
%               over the training examples if you are implementing it for the 
%               first time.
%
% Part 3: Implement regularization with the cost function and gradients.
%
%         Hint: You can implement this around the code for
%               backpropagation. That is, you can compute the gradients for
%               the regularization separately and then add them to Theta1_grad
%               and Theta2_grad from Part 2.
%


Y = [];
E = eye(num_labels);
for i = 1:num_labels,
    Y_t = find(y == i);
    Y(Y_t, :) = repmat(E(i, :), size(Y_t, 1), 1);
end;

% FP
X = [ones(m, 1) X];
a2 = sigmoid(X * Theta1');
a2 = [ones(m, 1) a2];
a3 = sigmoid(a2 * Theta2');


sg1 = [zeros(size(Theta1, 1), 1) Theta1(:, 2:end)];
sg2 = [zeros(size(Theta2, 1), 1) Theta2(:, 2:end)];
sg1 = sum(sg1 .^ 2);
sg2 = sum(sg2 .^ 2);

cost = Y .* log(a3) + (1 - Y) .* log(1 - a3);
J = -1/m * sum(cost(:)) + lambda/(2 * m) * (sum(sg1(:)) + sum(sg2(:)));

% gradient  BP

delte1 = zeros(size(Theta1));
delte2 = zeros(size(Theta2));

for i = 1:m,
    a1 = X(i, :)';
    z2 = Theta1 * a1;
    a2 = sigmoid(z2);
    a2 = [1; a2];
    z3 = Theta2 * a2;
    a3 = sigmoid(z3);
    err3 = zeros(num_labels, 1);
    for j = 1:num_labels,
        err3(j) = a3(j) - (y(i) == j);
    end;
    err2 = Theta2' * err3;
    err2 = err2(2: end) .* sigmoidGradient(z2);
    delte2 = delte2 + err3 * a2';
    delte1 = delte1 + err2 * a1';
end;

Theta1_t = [zeros(size(Theta1, 1), 1) Theta1(:, 2:end)];
Theta2_t = [zeros(size(Theta2, 1), 1) Theta2(:, 2:end)];

Theta1_grad = 1/m * delte1 + lambda/m * Theta1_t;
Theta2_grad = 1/m * delte2 + lambda/m * Theta2_t;













% -------------------------------------------------------------

% =========================================================================

% Unroll gradients
grad = [Theta1_grad(:) ; Theta2_grad(:)];


end
